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Full text of "Mathematical And Physical Papers - Iii"

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OJST THE MOTION  OF  PENDULUMS.
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augment the rate of decrease, which were not taken into account in the calculation.
77. Of Baily's pendulums I have compared the following with theory in regard to the decrement of the arc of vibration. No. 1 (the 1^-inch platina sphere), experiments 1 to 8 ; No. 3 (the brass IJ-inch sphere), experiments 9 to 16; No. 6 (the 2-inch brass sphere), experiments 33 to 40; No. 21 (the 0410 inch long copper cylindrical rod), experiments 109 to 112; and Nos. 3538 (the H-inch long brass tube), experiments 167 to 174 I have not thought it worth while to compute the results obtained with the other IJ-inch and 2-inch spheres, inasmuch as they were of the same size as the brass spheres, and moreover the observation of the decrement of the arc was not the object Baily had in view in making the experiments. The 3-inch sphere, and all the other cylindrical rods and combinations of cylindrical rods and spheres, belong to the " additional experiments " for which the arcs are not given.
The mode of performing the calculation will best be explained by an example. Take, for instance, the pair of experiments Nos. 1 and 2. In No. 1 the total interval was 4*22 hours, the initial arc was 0*77, the final arc 0'29, the mean height of the barometer 30'24 inches, and the temperature about 38 F. The difference of the common logarithms of the initial and final arcs is 0*424, and this divided by the total interval gives 01005 for the difference of logarithms for one hour. The second experiment, treated in a similar way, gives 0*0352, which expresses the effect of friction at the point of support, communication of motion to the support itself, &c., together with the resistance of highly rarefied air at a pressure of only 0*97 inch of mercury. Since we have reason to believe that p! is independent of the density, we may get the effect of air at a pressure of 30*24-0*97 or 29*27 inches of mercury by subtracting 0*0352 from 01005, which gives 0-005:1 Reducing to 29 inches of mercury for convenience of comparison, we get 0*0649. Each pair of experiments is to -be treated in the same way. Since the temperature was nearly the same in the experiments made with the same pendulum, we may suppose it constant, and equal to the mean of the temperatures in the experiments made under the full atmospheric pressure. The experiments reduced consist of four pair for each pendulum,
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